相关论文: Syzygies using vector bundles

Ein and Lazarsfeld have shown that one can read off the gonality of an algebraic curve from its syzygies in the embedding defined by any one line bundle of sufficiently large degree. This note extends their approach and shows that the…

Motivated by toric geometry, we lift machinery for understanding syzygies of curves in projective space to the setting of products of projective spaces. Using this machinery, we show an analogue of an influential result of Gruson, Peskine,…

A stratified space is a kind of topological space together with a partition into smooth manifolds. These kinds of spaces naturally arise in the study of singular algebraic varieties, symplectic reduction, and differentiable stacks. In this…

In this article we describe vector bundles over projectivoid line and show how it is similar to (and different) from Gorthendieck's classification of vector bundles over projective line.

The linear transports along paths in vector bundles introduced in Ref. [1] are applied to the special case of tensor bundles over a given differentiable manifold. Links with the transports along paths generated by derivations of tensor…

This paper is a survey of recent work on the asymptotic behavior of the syzygies of a smooth complex projective variety as the positivity of the embedding line bundle grows. After a quick overview of results from the 1980s and 1990s…

Moduli of vector bundles on stacky curves behave similarly to moduli of vector bundles on curves, except there are additional numerical invariants giving many different notions of stability. We apply the existence criterion for good moduli…

We give a proof of the existence of radial (smooth) parallel sections of vector bundles endowed with a linear connection.

We discuss phenomena of stabilization for direct images of line bundles over projective curves mapping onto the projective line, for maps of sufficiently big degree.

The present paper is related to a conjecture made by Green and Lazarsfeld concerning 1-linear syzygies of curves embedded by complete linear systems of sufficiently large degrees. Given a smooth, irreducible, complex, projective curve $X$,…

Classification theory and the study of projective varieties which are covered by rational curves of minimal degrees naturally leads to the study of families of singular rational curves. Since families of arbitrarily singular curves are hard…

Let $(X, H)$ be a polarized smooth projective algebraic surface and $E$ is globally generated, stable vector bundle on $X$. Then the Syzygy bundle $M_E$ associated to it is defined as the kernel bundle corresponding to the evaluation map.…

In this note we study curves (arrangements) in the complex projective plane which can be considered as generalizations of free curves. We construct families of arrangements which are nearly free and possess interesting geometric properties.…

We investigate orthogonal and symplectic bundles with parabolic structure, over a curve.

In this work we will prove results that ensure the simplicity and the exceptionality of vector bundles which are defined by the splitting of pure resolutions. We will call such objects syzygy bundles.

We study vector bundles on curves with rational tails and their smoothings and give a sufficient condition for the general fibre to be balanced.

We present equivalences between certain categories of vector bundles on projective varieties, namely cokernel bundles, Steiner bundles, syzygy bundles, and monads, and full subcategories of representations of certain quivers. As an…

In this note we make use of some properties of vector fields on a manifold to give an alternate proof to [3] for the equivalence between connections and parallel transport on vector bundles over manifolds. Out of the proof will emerge a new…

We present a geometric interpretation of tight closure in terms of vector bundles and projective bundles.

We show that on a generic curve, a bundle obtained by successive extensions is stable. We compute the dimension of the set of such extensions. We use degeneration methods specializing the curve to a chain of elliptic components